Preamble
Mathematical education should develop understanding and the ability to solve problems independently and collaboratively. The availability of AI changes the conditions for this from the start of university studies through to the doctorate. We must clarify which abilities will be needed and how they can be acquired and demonstrated. This paper sets out principles as a basis for shared discussion and experimentation.
We regard this position paper as a draft intended to encourage discussion of this complex topic, and reserve the right to substantially revise our positions as discussion and practical experimentation proceed.
Principles
01Personal development is an educational goal in its own right.
Mathematical education should foster personal development, imagination, self-determined action and judgement on societal matters. It helps people develop their own goals, see themselves as part of a community and assess the consequences of their actions. Personal development has value in its own right and must help shape degree programmes.
02The intended qualification determines the learning objectives.
The starting point is the work in society and research for which a degree programme should prepare students. This includes responsible problem-solving with AI: refining problems, selecting tools, and checking, interpreting and making use of results. The competencies that cannot be delegated must be identified. Conceptual understanding, evaluating arguments, and working with examples and counterexamples are starting points for a competency profile that remains to be developed. The required scope depends on the field of study and level of qualification. An important aim of doctoral study is to develop the ability to assess the prospects of success of research approaches.
03Communicating one’s own abilities and results is central
Mathematical education should enable students and doctoral researchers to communicate solutions and results. Writing, presenting and explaining are core competencies. AI use in this process must be transparently disclosed.
04Education must enable critical assessment of AI.
Responsible engagement with AI includes examining biases, the provenance of training data, questions of intellectual property, and social and ecological consequences. Students should be able to assess these conditions and make reasoned decisions about the use of AI. Different positions, including rejection of AI, must be taken seriously.
05Learning pathways must ensure the development of students’ own abilities.
The fact that an activity can later be delegated to AI does not determine whether practising it oneself is necessary for learning. At the same time, AI can help students acquire competencies that cannot be delegated, for example through explanations, follow-up questions and feedback. What matters is whether this develops their own understanding and independent judgement. Doctoral study in particular is a process of learning and development in which independent questioning, failure and the formation of judgement remain central.
06Human relationships and collaborative work remain a central part of education.
Personal encouragement, academic role models and a sense of belonging are important foundations of student motivation. Working together on problems also develops the ability to explain and listen, engage with criticism and take shared responsibility. Both require reliable opportunities to interact with teachers and fellow students throughout a degree programme.
07Assessment must make personal competence and responsible tool use visible.
When AI is available, correct results do not automatically demonstrate either understanding or individual contributions. Assessments must therefore make clear what students can do themselves and what they can achieve with tools. This also applies to final theses and doctorates; a doctorate must demonstrate the ability to conduct independent research. Responsibility for results remains with humans.
08Institutions must ensure fair conditions and clear rules.
Rules tied to learning objectives and disclosure of relevant AI use must apply to students and teachers alike. Required tools must be accessible irrespective of personal financial resources and with as few accessibility barriers as possible. Learning and research data must be protected; assessments and decisions must be transparent and understandable.
09Reform must be tried out and developed collaboratively.
Students, doctoral researchers and teachers must shape reform together and review it in light of new experiences. New forms of learning require time, qualified supervision and professional development. Their demands must be coordinated with the curriculum as a whole; new requirements must not simply be added to the existing workload.